Identification and Analysis of Instability in Non-Premixed
Swirling Flames using LES
K.K.J. Ranga Dinesh 1 , K.W. Jenkins 1 , M.P. Kirkpatrick 2 , W.Malalasekera 3
1. School Of Engineering, Cranfield University, Cranfield, Bedford, MK43 0AL,
UK.
2. School of Aerospace, Mechanical and Mechatronic Engineering, The
University of Sydney, NSW 2006, Australia.
3. Wolfson School of Mechanical and Manufacturing Engineering,
Loughborough University, Loughborough, Leicester, LE 11 3TU, UK.
Corresponding author: K.K.J.Ranga Dinesh
Email address: Ranga.Dinesh@Cranfield.ac.uk
Postal Address: School of Engineering, Cranfield University, Cranfield, Bedford,
MK43 0AL, UK.
Telephone number: +44 (0) 1234750111 ext 5350
Fax number: +44 1234750195
Revised manuscript prepared for the Journal of Combustion Theory and
Modelling
31st of July 2009
1
Identification and Analysis of Instability in Non-Premixed
Swirling Flames using LES
K.K.J. Ranga Dinesh 1 , K.W. Jenkins 1 , M.P. Kirkpatrick 2 , W.Malalasekera 3
ABSTRACT
Large eddy simulations (LES) of turbulent non-premixed swirling flames based on the
Sydney swirl burner experiments under different flame characteristics are used to
uncover the underlying instability modes responsible for the centre jet precession and
large scale recirculation zone. The selected flame series known as SMH flames have a
fuel mixture of methane-hydrogen (50:50 by volume). The LES solves the governing
equations on a structured Cartesian grid using a finite volume method, with
turbulence and combustion modelling based on the localised dynamic Smagorinsky
model and the steady laminar flamelet model respectively. The LES results are
validated against experimental measurements and overall the LES yields good
qualitative and quantitative agreement with the experimental observations. Analysis
showed that the LES predicted two types of instability modes near fuel jet region and
bluff body stabilized recirculation zone region. The Mode I instability defined as
cyclic precession of a centre jet is identified using the time periodicity of the centre jet
in flames SMH1 and SMH2 and the Mode II instability defined as cyclic expansion
and collapse of the recirculation zone is identified using the time periodicity of the
recirculation zone in flame SMH3. Finally frequency spectra obtained from the LES
are found to be in good agreement with the experimentally observed precession
frequencies.
Key words: LES, Swirl, Non-premixed combustion, Precession, Instability modes
2
1. INTRODUCTION
Swirl based applications in both reacting and non-reacting flows are widely used in
many engineering applications to achieve mixing enhancement, flame stabilisation,
ignition stability, blowoff characteristics, and pollution reduction. Many engineering
applications such as gas turbines, internal combustion engines, burners and furnaces
operate in a highly unsteady turbulent environment in which oscillations and
instabilities play an important role in determining the overall stability of the system.
Although details of oscillations in swirling isothermal and reacting flows have been
determined to some extent [1-2], a comprehensive multiscale, multipoint,
instantaneous flow structure analysis is still required to access the highly unsteady
physical processes that occur in swirl combustion systems. In isothermal swirling
flow fields, jet precession, recirculation, VB and a precessing vortex core (PVC) are
the main physical flow features that produce instability [3]. However, in combustion
systems, these phenomena can promote coupling between combustion, flow dynamics
and acoustics [4]. The identification of the oscillation modes and the effect of a PVC
on instability remains a challenge especially over a wide range of practical
engineering applications. For example, the interactions between different instability
oscillations can cause considerable acoustic fluctuations as a result of the pressure
field [5-7].
Since the current trend of swirl stabilised combustion systems is shifting towards lean
burn combustion to satisfy new emission regulations, combustion instability plays a
vital role and is frequently encountered during the development stage of swirl
combustion systems [5]. The most important instability driven mechanisms in gas
turbine type combustion configurations can be classified as flame-vortex interactions
3
[8-9], fuel/air ratio [10] and spray-flow interactions [11]. Several groups have studied
these mechanisms, for example, Richard and Janus [12] and Lee and Santavicca [13]
studied the combustion oscillations of a gaseous fuel swirl configuration, Yu et al.
[14] studied the instabilities based on acoustic-vortex flame interactions and Presser et
al. [15] studied the aerodynamics characteristics of swirling spray flames for
combustion instabilities. Lee and Santavicca [16] and Richards et al. [17] also studied
the active and passive control combustion instabilities for gas turbines combustors
respectively.
Extensive efforts have gone into performing numerical simulations of swirl stabilised
isothermal and reacting systems. Accurate predictions of large scale unsteady flame
oscillations, instability modes, PVC structure and the shear layer instability are very
demanding and therefore the high-fidelity numerical studies with advanced physical
sub-models are necessary. Progress in computing power and physical sub-modelling
has led to the expansion of numerical approaches to predict the instabilities in swirl
combustion systems [5]. Large eddy simulations (LES) are now widely accepted as a
potential numerical tool for solving large scale unsteady behaviour of complex
turbulent flows. In LES, the large scale turbulence structures are directly computed
and small dissipative structures are modelled. Encouraging results have been reported
in recent literature [18-21] which demonstrates the ability of LES to capture the
unsteady flow field in complex swirl configurations including multiphase flows and
combustion processes such as gas turbine combustion, internal combustion engines,
industrial furnaces and liquid-fueled rocket propulsion.
4
LES has been successfully used for turbulent non-premixed combustion applications
in fairly simple geometries and achieved significant accuracy. For example in gaseous
combustion, Cook and Riley [22] applied equilibrium chemistry, and Branley and
Jones [23] applied steady flamelet model with single flamelet, Venkatramanan and
Pitsch [24] and Kempf et al. [25] used a steady flamelet model with multiple flamelets
for LES combustion applications. Pierce and Moin [26] further extended the flamelet
model combined with progress variable and developed the so called flamelet/progress
variable approach. Navarro-Martinez and Kronenburg [27] have successfully
demonstrated the conditional moment closure (CMC) model for LES. Mcmurtry et al.
[28] applied the linear eddy model for combustion LES.
Additionally, LES has been used to study swirl stabilised combustion systems in order
to investigate the behaviour of flames under highly unsteady conditions. For example,
Huang et al. [29] reviewed LES for lean-premixed combustion with a gaseous fuel
and analysed details of combustion dynamics associated with swirl injectors. Pierce
and Moin [26] performed LES for swirling flames and accurately predicted the
turbulent mixing and combustion dynamics for a coaxial combustor. Kim and Syed
[30] and Di Mare et al. [31] performed LES calculations of a model gas turbine
combustor and found good agreement with experimental measurements. Selle et al.
[32] have conducted LES calculations in a complex geometry for an industrial gas
turbine burner. Grinstein and Fureby [33] examined the rectangular-shaped combustor
corresponding to General Electric aircraft engines using LES and found reasonable
agreement with experimental data and Mahesh et al. [34] conducted a series of LES
calculations for a section of the Pratt and Whitney gas turbine combustor and
validated the LES results against experimental measurements. Fureby et al. [35]
5
examined a multi-swirl gas turbine combustor using LES for the design of a future
generation of combustors. Bioleau et al. [36] used LES to study the ignition sequence
in an annular chamber and demonstrated the variability of ignition for different
combustor sectors and Boudier et al. [37] studied the effects of mesh resolution in
LES of flow within complex geometries encountered in gas turbine combustors.
The Sydney swirl burner flame series [38-41] effectively allows more opportunities
for computational researchers to investigate the complex flow physics and systematic
analysis of turbulence chemistry interactions for the laboratory scale swirl burner,
which contains features similar to those found in practical combustors. The swirl
configuration features a non-premixed flame stabilised by an upstream recirculation
zone caused by a bluff body and a second downstream recirculation zone induced by
swirl. A few attempts have already been made to model the Sydney swirling flame
series using numerous combustion models. Among them El-Asrag and Menon [42]
and James et al. [43] modelled flames with different combustion models. In earlier
studies, we have shown that LES predicts different isothermal swirling flow fields of
the Sydney swirl flame series with a good degree of success [44] and later extended
the work to the reacting cases [45]. We have also investigated flame comparisons
based on two different independent LES codes [46] and found good agreement
especially for capturing the vortex breakdown, recirculation, turbulence and basic
swirling flame structures. Despite these contributions and validation studies, a
systemic study of flow instabilities associated with the Sydney swirling flames is
essential and timely. Ranga Dinesh and Kirkpatrick [47] recently examined the
instability of isothermal swirling jets for a wide range of Reynolds and swirl numbers
and captured PVC structures, distinct precession frequencies and also found good
6
agreement with the experimental observations. Therefore the current work which is a
continuation of previous work [47] is focused on capturing the flame oscillations and
corresponding instability modes associated with the Sydney swirl burner SMH flame
series originally identified by Al-Abdeli et al. [41]. Here, we address the time
periodicity in the centre jet and the recirculation zone and the instability modes
associated with a centre jet and the bluff body stabilised recirculation zone. This
paper is organised as follows: Section 2 describes the mathematical formulations
associated with LES and is followed by the simulation details (section 3) and
experimental configuration (section 4). In section 5 we discuss the results for all three
flames (SMH1, SMH2 and SMH3) from low to high swirl numbers under different
flow conditions. Finally, we conclude the work in section 6 and suggest future work.
2. Mathematical Formulations
A. Filtered LES equations
In LES, the most energetic large flow structures are resolved, whereas the less
energetic small scale flow structures are modelled. A spatial filter is generally applied
to separate the large and small scale structures. For a given function f ( x, t ) the
filtered field f ( x, t ) is determined by convolution with the filter function G
f ( x)   f ( x' )G( x  x, ( x))dx ,
(1)

where the integration is carried out over the entire flow domain  and  is the filter
width, which varies with position. A number of filters are used in LES such as top hat
or box filter, Gaussian filter, spectral filter. In the present work, a so called top hat
filter (implicit filtering) having a filter-width  j proportional to the size of the local
cell is used. In turbulent reacting flows large density variations occur, which are
7
treated using Favre filtered variables, which leads to the transport equations for Favre
filtered mass, momentum and mixture fraction:
 u j

0
t
x j
(2)
 1  u i u j
  u i (  u i u j )
P  
 2  (   t )  




 x j xi
t
x j
xi x j 
2

 

1 
  ij kk    gi


3 x 
 1 u k  

   ij
3

x
 
k

(3)
j
 f



u j f 
t
x j
x j


    t  f 
   

    t  x j 
(4)
In the above equations  represents the density, ui is the velocity component in xi
direction, p is the pressure,  is the kinematics viscosity, f is the mixture fraction,
 t is the turbulent viscosity,  is the laminar Schmidt number,  t is the turbulent
Schmidt number and  kk is the isotropic part of the sub-grid scale stress tensor. An
over-bar describes the application of the spatial filter while the tilde denotes Favre
filtered quantities. The laminar Schmidt number was set to 0.7 and the turbulent
Schmidt number for mixture fraction was set to 0.4. Finally to close these equations,
the turbulent eddy viscosity  t in Eq. (3) and (4) has to be evaluated using a model
equation.
B. Modelling of turbulent eddy viscosity
The Smagorinsky eddy viscosity model [48] is employed to calculate the turbulent
eddy viscosity t . The Smagorinsky eddy viscosity model [48] uses a model
parameter C s , the filter width  and strain rate tensor S i , j such that
8
2
 t  Cs  S i , j  Cs 
2
1  ui u j 



2  x j xi 
(5)
The model parameter Cs is obtained using the localised dynamic procedure of
Piomelli and Liu [49].
C. Modelling of combustion
In LES, chemical reactions occur at the sub-grid scales and therefore modelling is
required for combustion chemistry. Here an assumed probability density function
(PDF) for the mixture fraction is chosen as a means of modelling the sub-grid scale
mixing with  PDF used for the mixture fraction. The functional dependence of the
thermo-chemical variables is closed through the steady laminar flamelet approach. In
this approach the variables such as density, temperature and species concentrations
depend on Favre filtered mixture fraction, mixture fraction variance and scalar
dissipation rate. The sub-grid scale variance of the mixture fraction is modelled using
the gradient transport model. The flamelet calculations were performed using the
Flamemaster code developed by Pitsch [50], which incorporates the GRI 2.11
mechanism with detailed chemistry [51].
3. Simulation Details
In the current work all simulations are performed using the PUFFIN code developed
by Kirkpatrick et al. [52-54] and later extended by Ranga Dinesh [55]. PUFFIN
computes the temporal development of large-scale flow structures by solving the
transport equations for the Favre-filtered continuity, momentum and mixture fraction.
The equations are discretised in space with the finite volume formulation using
Cartesian coordinates on a non-uniform staggered grid. Second order central
9
differences (CDS) are used for the spatial discretisation of all terms in both the
momentum equation and the pressure correction equation. This minimizes the
projection error and ensures convergence in conjunction with an iterative solver. The
diffusion terms of the scalar transport equation are also discretised using the second
order CDS. However, discretisation of convection term in the mixture fraction
transport equation using CDS would cause numerical wiggles in the mixture fraction.
To avoid this problem, here we employed a Simple High Accuracy Resolution
Program (SHARP) developed by Leonard [56].
In order to advance a variable density calculation, an iterative time advancement
scheme is used. First, the time derivative of the mixture fraction is approximated
using the Crank-Nicolson scheme. The flamelet library yields the density and
calculates the filtered density field at the end of the time step. The new density at this
time step is then used to advance the momentum equations. The momentum equations
are integrated in time using a second order hybrid scheme. Advection terms are
calculated explicitly using second order Adams-Bashforth while diffusion terms are
calculated implicitly using second order Adams-Moulton to yield an approximate
solution for the velocity field. Finally, mass conservation is enforced through a
pressure correction step. Typically 8-10 outer iterations of this procedure are required
to obtain satisfactory convergence at each time step. The time step is varied to ensure
that the Courant number Co  tui xi remains approximately constant where xi is
the cell width, t is the time step and u i is the velocity component in the xi
direction. The solution is advanced with a time step corresponding to a Courant
number in the range of Co  0.3 to 0.6.
10
The Bi-Conjugate Gradient Stabilized
(BiCGStab) method with a Modified Strongly Implicit (MSI) preconditioner is used
to solve the system of algebraic equations resulting from the discretisation.
Simulations for the flames SMH1 and SMH2 were carried out with the dimensions of
300  300  250mm in the x,y and z directions respectively and employed nonuniform Cartesian grids with 3.4 million cells. Since the flame SMH3 has high fuel jet
velocity, it produces a longer flame than both the SMH1 and SMH2 in the streamwise
direction, we therefore used a larger domain for the axial direction such
that 300  300  400mm which employed 4 million cells.
The mean axial velocity distribution for the fuel inlet and mean axial and swirling
velocity distributions for air annulus are specified using power low profiles;

y
 U  1.218U j 1  
 

1/ 7
(6)
where U j is the bulk velocity, y is the radial distance from the jet centre line and
  1.01R j , where R j is the fuel jet radius of 1.8 mm. The factor 1.01 is included to
ensure that velocity gradients are finite at the walls. The same equation is used for the
swirling air stream with U j replaced by bulk axial velocity U s and bulk tangential
velocity Ws and y being the radial distance from the centre of the annulus and
  1.01 times the half width of the annulus.
Velocity fluctuations are generated from a Gaussian random number generator, which
are then added to the mean velocity profiles such that the inflow has the same
turbulence kinetic energy levels as that obtained from the experimental data. A top hat
profile is used as the inflow condition for the mixture fraction. A Free slip boundary
11
condition is applied at the solid walls and at the outflow plane, a convective outlet
boundary condition is used for the velocities and a zero normal gradient condition is
used for the mixture fraction. All computations were carried out for a sufficient time
to ensure we achieved converged solutions, and the total time for each simulation is
0.24s.
4. Experimental Configuration
The Sydney swirl burner configuration shown in Figure 1, which is an extension of
the well-characterized Sydney bluff body to the swirling flames. Extensive details
have been reported in the literature for the Sydney swirling flames including flow
field and compositional structures for pure methane flames [38], stability
characteristics [39], compositional structure [40] and time varying behaviour [41].
The burner has a 60mm diameter annulus for a primary swirling air stream
surrounding a circular bluff body of diameter D=50mm and the central fuel jet is
3.6mm in diameter. The burner is housed in a secondary co-flow wind tunnel with a
square cross section with 130mm sides. Swirl is introduced aerodynamically into the
primary annulus air stream at a distance 300mm upstream of the burner exit plane and
inclined 15 degrees upward to the horizontal plane. The swirl number can be varied
by changing the relative magnitude of the tangential and axial flow rates. The
literature already includes the details of flame conditions and can be found in [38-41].
In the present LES calculations, the SMH flames were modelled burning a methanehydrogen fuel mixture (50:50 by volume). The properties of the simulated flames are
summarised in table 1. Here, U j (m / s ) , U s (m / s) , Ws (m / s) , U e (m / s) , S g , and
12
Re are fuel jet velocity, axial velocity of the primary annulus, swirl velocity of the
primary annulus, secondary co-flow velocity, swirl number and Reynolds number of
the fuel jet respectively.
Case
Fuel
U j (m / s)
U s (m / s)
Ws ( m / s )
U e (m / s)
Sg
Re
SMH1
CH 4  H 2
140.8
42.8
13.8
20.0
0.32
19,300
SMH2
CH 4  H 2
140.8
29.7
16.0
20.0
0.54
19,300
SMH3
CH 4  H 2
226.0
29.7
16.0
20.0
0.54
31,000
Table 1. Details about the characteristics properties of SMH flame series
5. Results and Discussion
The Sydney swirl burner is designed to study the reacting and non-reacting swirling
flow structures for a range of swirl, Reynolds numbers and fuel mixtures. The aim
here is to uncover the time periodicity in the centre jet and bluff body stabilised
recirculation zone and the corresponding precession frequencies while identifying the
dominant instability modes for all three swirling flames. Here we have considered the
SMH flame series which contains three different swirling flames known as SMH1,
SMH2 and SMH3 for three different Reynolds and swirl numbers [39-41]. Since
validation of LES results with experimental measurements is necessary, first we
address the comparisons between LES computations and the experimental
measurements. The second part is a discussion of the existence of instability modes in
which we analyse the time periodicity in both the centre jet and bluff body stabilised
recirculation zone.
13
5.1 Validation studies
Figures 2-4 show snapshots of filtered temperatures for SMH1, SMH2 and SMH3
respectively. The high temperature distribution region in the bluff body stabilized
recirculation zone is much wider for both SMH1 and SMH3 flames thinner for the
SMH2 flame. The strong and weak neck zones are visible in SMH1 and SMH3
respectively. The neck zones of flames SMH1 and SMH3 appear approximately
60mm and 50mm downstream from the burner exit plane respectively.
Shown in Figure 5 is the time averaged mean axial velocity at different axial
locations. The comparisons are presented for x/D=0.2,0.8,1,6 and 3.5 for SMH1 (left
side) and x/D=0.136,0.4,1.2 and 2.5 for SMH2 (right side). The experimental data
shows that for both flames the bluff body stabilised recirculation zone is extending
axially up to x/D=1.2 from the burner exit plane [39]. The occurrence of the negative
mean axial velocity values at x/D=0.136, 0.2, 0.4 and 0.8 indicates a flow reversal
which is well captured by the LES. However, the calculations over estimate the
centerline mean axial velocity at x/D=1.6,3.5 for SMH1 and at x/D=2.5 for SMH2.
This is most likely attributed to the difference in momentum decay in the central jet
with the LES centre jet breakdown slower than that found in the experiment.
Figure 6 shows comparison between numerical and experimental results for the time
averaged mean swirling velocity (left side: SMH1, right-side: SMH2). The
comparison between calculations and measurements are very good for flame SMH1
and reasonably good for flame SMH2. The LES results captured well the peak values
which appear in the shear layers between the centre jet and the recirculation zone and
also the outer flow region and the recirculation zone. However, the mean swirl
14
velocity of SMH2 (right side) has some over prediction at x/D=1.2 and 2.5 and this
may be attributed to the differences of swirl momentum decay in experimental and
numerical results. Comparison between LES calculations and the experimental
measurements for the rms (root mean square) axial velocity is shown in Figure 7. The
LES results under predict at x/D=0.2,0.8 and over predict at x/D=1.6,3.5 for flames
SMH1 and SMH2 respectively.
Finally, Figures 8-10 show the comparison of the mean temperature, CO2 and CO
mass fractions (left side: SMH1, right-side: SMH2). Despite the complexity of the
flow field, the comparison of the temperature field is reasonable at most axial
locations for both flames. The CO2 (Figure 9) profiles follow the same behaviour as
temperature for both flames where the LES over predicts the CO2 value at x/D=0.2.
Similar to the temperature distributions, the computed CO2 under predicts at x/D=0.8
and the peak values are not accurately captured for the SMH1 flame. For CO (Figure
10), the radial spread is underestimated only at x/D=0.2 for both flames. Further
downstream the comparisons are very good. Given the complexity of the flame and
flow field, LES calculated species concentrations are in good agreement with the
experimental data.
In summary, the flames studied here involve a complex flow situation and flame
structures in which there occurs recirculation, centre jet precession, shear layer
instability and complex turbulence chemistry interactions. The computed flow and
scalar patterns agree well with the experimental data and hence this validation allows
us to succeed our main goal “identification of instability modes associated with SMH
flame series”.
15
5.2 Time periodicity in the centre jet of flame SMH1
This section discusses the centre jet precession of flame SMH1 using the LES data
that has been originally identified by Al-Abdeli et al. [41] in their experimental
investigation for the Sydney swirl burner experimental data base managed by Masri’s
group [40].
Figure 11 (a-h) shows a series of snapshots (filtered axial velocity) at different
periodic time intervals generated from the LES. From the experimental work, AlAbdeli et al. [41] observed a periodic (cyclic) precession motion of the centre jet for
flame SMH1 which was defined as Mode I instability using snapshots at different
time periods. Similarly here we used the snapshots of filtered axial velocity to
demonstrate the Mode I instability in flame SMH1.
The calculated images from (a) to (h) in Figure 11 show the periodic variation of the
centre jet. For example, Figure 11 (a) shows a snapshot of the filtered axial velocity
which is vertical at that particular time. Then slowly starts to shift towards one side of
the centerline (b-c) and then return again in (d). The centre jet is then seen to cross
over to other side (e-g), and finally reaching the starting position of (a) in the last
snapshots (h). Since Mode I instability is believed to be a consequence of an orbital
(circular) motion about the central axis the observations from Figure 11 can be
defined as Mode I instability. It is important to note that the Mode I instability has
also been identified in Sydney isothermal swirling flows both numerically by Ranga
Dinesh and Kirkpatrick [47] and experimentally by Al-Abdeli and Masri [57]. In the
current case, vortex shedding due to hydrodynamic instability might be the same as
that is in the isothermal case, but the complexity of the Mode I instability increases
16
due to combustion heat release, which eventually increases the unsteady frequencies.
The visualisation of Mode I instability of flame SMH1 in a plane perpendicular to the
centreline is shown in Figure 12. Figures 12 aa, cc and gg show the snapshots of the
filtered axial velocity in a normal plane correspond to Figures 11 a, c and g. The axial
location of the considered horizontal plane for Figure 12 is marked by a line in Figure
11 c. Figures 11 and 12 indicate that the swirling motion rotates the centre jet around
the axis as cyclic motion and thus forms PVC structures in the near region of the jet.
A further investigation to determine the changes of the heat release respect to centre
jet precession frequency for different swirl numbers should be performed to
investigate the rapid changes in the instantaneous temperature field.
In order to analyse the time periodicity in the centre jet, a spatial jet locator must be
considered and here we have a spatial jet locator which is positioned just off the
burner centerline such that x=12.3mm (axial location) and r=2.3mm (radial location)
which is similar to the experimental location [41]. A pair of monitoring points either
side of the centre jet are considered, and we constructed a power spectrum by
applying the Fast Fourier Transform (FFT) for the instantaneous filtered axial
velocity. Figure 13 shows the power spectrum of SMH1 at the spatial jet locator with
several peaks at low frequency levels and peaks become more discrete and appear
around ~50Hz. Al-Abdeli et al. [41] used three different experimental techniques to
detect distinct frequencies such as Laser Mie scattering, Shadowgraphs and LDV
(Laser Doppler Velocimetry) spectra. For SMH1 flame, Al-Abdeli et al. [41], detected
distinct frequencies for Mode I instability such that ~ 47Hz from Laser Mie
scattering, ~ 47Hz from Shadowgraphs and 41  58Hz from LDV spectra (Laser
17
Doppler Velocimetry). Therefore the distinct frequency found by LES calculation
(~50Hz) is in agreement with that found in the experimental investigation.
5.3 Time periodicity in the centre jet of flame SMH2
Snapshots of the filtered axial velocity for eight different time periods from the LES
are shown in Figure 14 (a-h). The SMH2 flame has relatively higher swirl number
( S g  0.54 ) than SMH1 and hence it exists a higher centrifugal force than that in
flame SMH1. Again, Al-Abdeli et al. [41] found a cyclic variation of the centre jet
which defined as Mode I instability. Figure 14 (a) indicates a vertical (straight) centre
jet which then starts to move to one side till Figure 14 (c). The jet then starts to move
to other side from Figure 14 (e) and finally move back to its initial position in Figure
14 (h). Since LES has captured this periodic centre jet precession we can refer this
motion as Mode I instability [41]. Furthermore, as seen in Figure 14 the centre jet of
flame SMH2 appears to shift more radially in both directions than that found in
SMH1. This can be expected since SMH2 has high centrifugal force than SMH1 due
to the high swirl number. Figure 15 shows the occurrence of Mode I instability of
flame SMH2 in a plane perpendicular to the centreline. Figures 15 aa, cc and ff show
the cross sectional snapshots corresponding to Figures 14 a, c and f respectively. The
location of the horizontal plane has been marked by a line in Figure 14 c. As seen in
Figure 15 snapshots of the filtered axial velocity in a horizontal plane (normal to
snapshots in Figure 11) again exhibit precession behaviour.
The power spectrum of flame SMH2 at the spatial jet locator defined in the previous
section is shown in Figure 16. Similar to SMH1, the power spectrum of flame SMH2
also shows peaks at low frequency levels with the peaks becoming more distinct
18
around ~47Hz. The distinct precession frequencies from the simulation demonstrate
the Mode I instability of flames SMH2 given by the cyclic variation of the centre jet.
Again, Al-Abdeli et al. [41] experimentally found distinct precession frequencies for
Mode I instability such that ~ 55Hz from Laser Mie scattering, ~ 55Hz from
Shadowgraphs and 48  58Hz from LDV spectra.
5.4 Time periodicity in the recirculation zone of flame SMH3
Here we discuss the time varying behaviour of flame SMH3 as well as another Mode
of instability this time associated with bluff body stabilised recirculation zone
originally identified by Al-Abdeli et al. [41]. It is important to note that the Mode II
instability was only identified for a few of the Sydney swirling flames depend on the
conditions that have been adopted to produce the flame. The Mode II instability
appears to be rather weak, but can still be seen for SMH3 flame. The cyclic oscillation
which appears in flame SMH3 defined as Mode II which can be described as the
expansion and collapse of the bluff body stabilised recirculation zone which is also
known as “puffing” motion.
To demonstrate the Mode II instability based on the LES data, we use six snapshots of
the filtered axial velocity (Figure 17 (a-f)) which only shows the negative axial
velocity which clearly indicates the region of the upstream recirculation zone at
different time periods. In addition, we generated the power spectrum for a particular
location at the envelope of the recirculation zone. Figure 17 shows the contour plots
of filtered axial velocity for the bluff body stabilised recirculation zone, where a solid
line indicates the boundary of the recirculation zone and the dashed lines indicate the
negative filtered axial velocity inside the recirculation zone. The ranges of contour
19
values (0 m/s to -20 m/s) are shown in Figure 17 (a). Figure 17 (a) at one particular
time shows a recirculation zone which continues to reduce over the next two time
intervals shown in Figures 17 (b) and (c) respectively. The recirculation zone then
starts to expand in Figure 17 (d) and (e) and eventually forms a similar shape as initial
snapshot in Figure 17 (f). Thus the time dependent snapshots show a sequential
collapse/contraction and then expansion of the bluff body stabilised recirculation zone
similar to that found in the experimental observation and can be referred as “puffing”
motion, defined as Mode II instability [41]. The expansion and collapse of the bluff
body stabilised recirculation zone has only been identified in some of the Sydney
swirling flames including SMH3.
This might occur due to coupling between
combustion heat release and flow velocities that have been adopted. Furthermore, the
Mode II instability has not been identified in Sydney swirling isothermal flow fields
either numerically [47] or experimentally [57]. Hence the identification of Mode II
instability (extension and collapse of the bluff body stabilised recirculation zone) both
numerically and experimentally can add a new dimension to the already existing
physical aspects of swirling flows [3] and thus help to derive a correlation between
flow reversal, mixing rate and temperature gradient. However, more investigation is
still needed both numerically and experimentally to reveal a major correlation for this
finding and we are keen to extend the present work to derive a mechanism for the
combustion instability based on flow reversal, mixing rate and temperature gradient
specifically for the flame SMH3.
Figure 18 shows the power spectrum of SMH3 at the envelope of the bluff body
stabilised recirculation zone. In order to analyse the time periodicity in this case the
recirculation zone, a pair of monitoring points around the envelope of the bluff body
20
stabilised recirculation zone are considered, which is similar to the experimental case
[41]. Again, the power spectrum is constructed by applying the Fast Fourier
Transform (FFT) for the instantaneous filtered axial velocity. The power spectrum of
flame SMH3 shows some peaks at low frequency levels and peaks become more
distinct around ~40-60Hz. The peaks around ~40-60Hz are attributed to the Mode II
instability, and the identification of these peaks of Mode II unsteadiness further
demonstrates the usefulness of the LES technique for simulation of complex unsteady
flames and combustion dynamics. The experimental group revealed [41] the distinct
precession frequencies for Mode II instability such that shadowgraphs found the
distinct precession frequency of ~ 60Hz and LDV spectra found the range 63  67Hz .
6. Conclusions
We have performed LES of turbulent swirl flames known as SMH1, SMH2 and
SMH3 and investigated the instabilities associated with each flames experimentally
conducted by Masri and co-workers [39-41]. The LES technique was applied
successfully to study the flame oscillations and instability modes originally identified
by Al-Abdeli et. al. [41].
First we compared the LES results with experimental data and found that results are in
good agreement for both velocity and scalar fields. Then we investigated the
instability mechanisms associated with the SMH flame series. The unsteady data from
the simulations along with the Fast Fourier Transform (FFT) algorithm have been
used for data analysis. Various snapshots and power spectra indicate the time
periodicity in the centre jet and the time periodicity in the recirculation zone. The
simulations captured the Mode I instability for both SMH1 and SMH2 flames in
21
which the instability involves precession of the centre jet. The power spectra
produced at the spatial jet locator further demonstrates the link between precession
frequencies and the Mode I instability for both flames. Another Mode of instability is
shown to be associated with large scale unsteadiness of the recirculation zone
characterized by “puffing” motion in flame SMH3. This has been referred as Mode II
instability and has not been identified in isothermal jets [47][57]. The identification of
two types of instability modes associated with these flames demonstrates that the LES
technique is useful and promising tool to capture the instabilities in complex turbulent
non-premixed flames. Although we have performed all simulations in incompressible
pressure based low Mach number variable density algorithm, the effect of
compressibility cannot be ruled out as a results of high fuel jet velocities for all three
flames. Therefore, the numerically computed pressure oscillations and the heat release
patterns might have some discrepancies with experimental values and thus make
differences for the distinct precession frequencies as appeared in the power spectra. In
addition, the rate of energy transfer to a fluctuation depends on the fluctuation itself
and this may be able to deviate the computed distinct frequencies with experimentally
observed values. However, the identification of Mode I and II instabilities both
computationally and experimentally provide useful details for the presence of
instabilities in turbulent non-premixed swirling flames and also highlights the
differences compared with the hydrodynamic instability.
The future numerical work will study the effect of swirl on combustion dynamics
which will lead to the identification of more flow features and coupling relations
between vortex breakdown, turbulence intensity, flame temperature and more
22
importantly the behaviour of the already existing instability modes bearing in mind
that the excessive swirl may lead to the occurrence of flame flashback.
Since the combustion phenomena in LES acts in small scales the energy transfer from
large scale to small scale along with heat release can be critically affected by the swirl
number. In such situations, the flame is anchored by the recirculating flow and
occurrence of the precession motion as observed in this investigation might cause
intermittency in the temperature field. An effort is currently underway to fully
investigate the effect of swirl on combustion intermittency for this burner
configuration and results will be reported in the near future.
23
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29
Figure Captions
Figure 1: Schematic drawing of the Sydney swirl burner
Figure 2: Snapshots of the filtered temperature for flame SMH1
Figure 3: Snapshots of the filtered temperature for flame SMH2
Figure 4: Snapshots of the filtered temperature for flame SMH3
Figure 5: Comparison of mean axial velocity for flame SMH1 (left side) and SMH2
(right side). Line denotes LES data and symbols denote experimental data.
Figure 6: Comparison of mean swirling velocity for flame SMH1 (left side) and
SMH2 (right side). Line denotes LES data and symbols denote experimental data.
Figure 7: Comparison of rms axial velocity for flame SMH1 (left side) and SMH2
(right side). Line denotes LES data and symbols denote experimental data.
Figure 8: Comparison of mean temperature for flame SMH1 (left side) and SMH2
(right side). Line denotes LES data and symbols denote experimental data.
Figure 9: Comparison of CO2 for flame SMH1 (left side) and SMH2 (right side). Line
denotes LES data and symbols denote experimental data.
30
Figure 10: Comparison of CO for flame SMH1 (left side) and SMH2 (right side).
Line denotes LES data and symbols denote experimental data.
Figure 11: Mode I instability in flame SMH1 identified using LES
Figure12. Mode I instability of flame SMH1 in a plane perpendicular to the centreline
Figure 13: Power spectrum of the flame SMH1 at spatial jet locator
Figure 14: Mode I instability in flame SMH2 identified using LES
Figure15. Mode I instability of flame SMH2 in a plane perpendicular to the centreline
Figure 16: Power spectrum of the flame SMH2 at spatial jet locator
Figure 17: Mode II instability in flame SMH3 identified using LES
Figure 18: Power spectrum of the flame SMH3 at envelope of the recirculation zone
31
Figures
Figure 1. Schematic drawing of the Sydney swirl burner
32
0.25
T(k)
1900
1800
1700
1600
1500
1400
1300
1200
1100
1000
900
800
700
600
500
400
Axial distance (m)
0.2
0.15
0.1
0.05
0
-0.1
-0.05
0
0.05
0.1
0.15
Radial distance (m)
Figure 2: Snapshots of the filtered temperature for flame SMH1
0.25
T(k)
1900
1800
1700
1600
1500
1400
1300
1200
1100
1000
900
800
700
600
500
400
Axial distance (m)
0.2
0.15
0.1
0.05
0
-0.1
-0.05
0
0.05
0.1
0.15
Radial distance (m)
Figure 3: Snapshots of the filtered temperature for flame SMH2
33
0.4
T(k)
1900
1700
1500
1300
1100
900
700
500
300
Axial distance (m)
0.3
0.2
0.1
0
-0.1
0
0.1
0.2
Radial distance (m)
Figure 4: Snapshots of the filtered temperature for flame SMH3
34
0.3
x/D=0.2
100
100
5050
50
00
0
0
0.5
1
00
100
100
50
50
0
0
0.5
1.5
x/D=1.6
0
x/D=
0.5
1
x/D=1.2
x/D=0.4
x/D=0
100
50
0
0.5
0.5
11
1.5
1.5
0
0.5
1
x/D=2.5
x/D=
x/D=1.2
150
100
100
100
50
50
50
50
0
00
0.5
1
1.5
0
0
0
0.5
0.5
x/D=3.5
150
100
50
0
0.5
1
r/R
1
1
1.5
1.5
x/D=2.5
100
<U> m/s
<U> m/s
1.51.5
50
00
<U> m/s
<U> m/s
1
100
0
11
00
150
0
0.5
0.5
150
100
<U> m/s
<U> m/s
1.5
x/D=0.8
150
150
100
100
50
0
x/D=0.4
x/D=0.136
150
150
<U> m/s
<U> m/s
150
0
50
0
0
0
0.5
1
1.5
0
r/R
r/R
Figure 5: Comparison of mean axial velocity for flame SMH1 (left side) and SMH2
(right side). Line denotes LES data and symbols denote experimental data.
35
1
x/D=
100
50
1.5
0.5
0.5
r/R
1
40 40
x/D=0.2
x/D=0.4
x/D=0.136
20
20 20
20
10
10 10
10
0
0 0
0
0.5
1
1.5
-10-10
0 0
0.50.5
1 1
40
40
30
20
0
0
-100
40
-100
4030
-10
0
1.5
x/D=1.6
20
1
0.5
1
1.5
-10
0
0.5
1
1.5
x/D=1.2
x/D=2.5
30
x/D=1.
20
10
10
10
0
40
0.5
20
10
-100
x/D=0.
0
3020
<W> m/s
<W> m/s
30
30
10
0
1
1
10
10
0.5
0.5
20
20
10
-10
0
20
30
<W> m/s
<W> m/s
30
1.51.5
x/D=0.4
x/D=1.2
40
x/D=0.8
x/D=0
30
30 30
-100
0
0
0.5
1
1.5
-10-10
0 0
0
0.50.5
r/R
11
1.51.5
-10
0
0.5
1
30
30
x/D=3
x/D=2.5
x/D=3.5
<W> m/s
30
<W> m/s
40
30
<W> m/s
<W> m/s
40
20
10
20
20
10
10
0
0
0
-100
0.5 r/R 1
1.5
-10
0
0.5
1
1.5
-10
0
r/R
Figure 6: Comparison of mean swirling velocity for flame SMH1 (left side) and
SMH2 (right side). Line denotes LES data and symbols denote experimental data.
36
0.5
r/R
1
30
x/D=0.2
30
r.m.s.(u) m/s
r.m.s.(u) m/s
30
20
0.5
0.5
1
1
1.5
1.5
x/D=0.4
x/D=1.2
r.m.s.(u) m/s
r.m.s.(u) m/s
10
0.5
1
1010
10
0.5
0.5
1
1
1.5
1.5
0.5
1
1.5
20
10
10
10
0.50.5r/R 1 1
1.51.5
30
20
10
00
0.5 r/R 1
0.5
1
00
x/D=1.7
0.5
1
30
x/D=3.5
x/D=2.5
x/D=3.5
r.m.s.(u) m/s
r.m.s.(u) m/s
30
00
20
20
0000
x/D=0.8
30
x/D=1.2
x/D=2.5
r.m.s.(u) m/s
10
1
40
20
0
00 0
30
0.5
30
30
20
00
2020
1.5
x/D=1.6
30
00
10
3030
20
00
10
0
00 0
40
1.5
x/D=0.8
30
r.m.s.(u) m/s
1
x/D=0.2
20
10
0.5
40
30
20
20
10
00
x/D=0.136
x/D=0.4
1.5
20
20
10
10
00
0.5
1
1.5
00
r/R
Figure 7: Comparison of rms axial velocity for flame SMH1 (left side) and SMH2
(right side). Line denotes LES data and symbols denote experimental data.
37
0.5
r/R
1
2000
x/D=0.2
T(k)
0.5
1
x/D=0.8
T(k)
1500
1000
00
0.5
2000
500
500
00
0
2000
2000
500
0.5
0.5
11
x/D=1.1
x/D=0.8
x/D=1.6
1500
1000
500
00
0
0.5
0.5
2000
2000
11
x/D=2.5
x/D=1.6
T(k)
T(k)
0
0.5
2000
x/D=
1000
500
0.5
500
00
0
1
500
0.5
0.5
r/R
11
0
2000
2000
x/D=3.5
x/D=3.5
1500
T(k)
T(k)
1500
1000
1000
500
500
00
x/D
1500
1000
1000
500
0.5
500
1500
1500
1000
0
2000
1500
1500
1
1500
00
1000
1000
1000
500
500
x/D=
1500
1000
1000
500
2000
T(k)
1000
00
2000
x/D=0.2
x/D=0.5
1500
1500
T(k)
1500
2000
2000
0.5
0
1
0.5
1
r/R
r/R
Figure 8: Comparison of mean temperature for flame SMH1 (left side) and SMH2
(right side). Line denotes LES data and symbols denote experimental data.
38
0.5
r/R
0.08
0.06
0.060.06
0.06
0.04
0.040.04
0.04
0.02
0.020.02
0.02
0.5
1
00 0
0
0.1 0.1
0.5
0.5
11
1.5
00
0.08
0.080.08
0.08
0.06
0.060.06
0.06
0.04
0.040.04
0.04
0.02
0.020.02
0.02
0.5
00 0
0
1
x/D=1.6
0.5
0.5
0.10.1
11
1.5
00
0.08
0.06
0.06
0.06
0.06
0.04
0.04
0.04
0.02
0.02
0.02
Y CO2
0.08
0.08
0.02
00
0.5
0000
1
0.1
0.1
0.5
r/R
0.08
0.06
0.06
Y CO2
0.08
00
0.04
0.02
0.02
00
1.5
x/D=3.5
x/D=3.5
0.04
1 1
0.5
00
1
0.5
1
1.5
r/R
r/R
Figure 9: Comparison of CO2 for flame SMH1 (left side) and SMH2 (right side). Line
denotes LES data and symbols denote experimental data
39
0.5
1
x/D
0.5
1
0.1
x/D=1.6
x/D=2.5
0.08
0.04
x/D=
0.1
x/D=1.1
x/D=0.8
Y CO2
x/D=0.8
0.1
Y CO2
0.1
x/D=0.5
x/D=0.2
0.080.08
00
Y CO2
0.1 0.1
0.08
00
0.1
Y CO2
x/D=0.2
Y CO2
Y CO2
0.1
x/D
0.5
r/R
1
0.08
0.06
0.06
0.06
0.06
0.04
0.04
0.04
0.04
0.02
0.02
0.02
0.02
0.5
1
0.5
0.5
1
1
1.5
x/D=1.1
x/D=0.8
00
0.1
0.08
0.08
0.08
0.06
Y CO
x/D=0.8
00
00
0.1
0.1
0.08
0.06
0.06
0.06
0.04
0.04
0.04
0.02
0.02
0.02
0.04
00
0.5
0.1
00 0
0
1
x/D=1.6
0.5
0.5
0.10.1
11
1.5
00
0.08
0.06
0.06
0.06
0.06
0.04
0.04
0.04
0.02
0.02
0.02
Y CO
0.08
0.08
0.04
00
0.5
00 0
0
1
0.5
0.5
r/R
1.5
00
0.1
0.1
x/D=3.5
x/D=3.5
0.08
0.06
0.06
Y CO
0.08
0.04
0.04
0.02
0.02
00
11
0.5
00
1
0.5
1
1.5
r/R
r/R
Figure 10: Comparison of CO for flame SMH1 (left side) and SMH2 (right side).
Line denotes LES data and symbols denote experimental data
40
x/
0.5
1
x/D
0.5
1
0.1
x/D=2.5
x/D=1.6
0.08
0.02
Y CO
0.1
x/D=0.5
x/D=0.2
0.08
0.08
0.02
Y CO
0.1
0.1
0.08
00
0.1
Y CO
x/D=0.2
Y CO
Y CO
0.1
x/D
0.5
r/R
1
a
e
b
c
d
f
g
h
Figure 11. Mode 1 instability in flame SMH1 identified using LES visualised by
filtered axial velocity
41
aa
cc
gg
Figure 12. Mode I instability of flame SMH1 in a plane perpendicular to the
centreline
Figure 13. Power spectrum of the flame SMH1 at spatial jet locator
42
a
e
b
c
f
d
g
h
Figure 14. Mode 1 instability in flame SMH2 identified using LES visualised by
filtered axial velocity
43
aa
cc
ff
Figure 15. Mode I instability of flame SMH2 in a plane perpendicular to the
centreline
Figure 16. Power spectrum of the flame SMH2 at spatial jet locator
44
U (m/s)
0
-5
-10
-15
-20
a
d
b
c
e
f
Figure 17. Mode II instability in flame SMH3 identified using LES visualised by
filtered axial velocity
45
Figure 18. Power spectrum of the flame SMH3 at envelope of the recirculation zone
46